This invention relates to an improvement of an electronic musical instrument of a harmonic synthesis type wherein a fundamental wave (basic tone) corresponding to the tone pitch of an operated key in a keyboard and respective components of its harmonic waves (over tones) are multiplied with corresponding amplitude coefficients respectively and then the multiplication products are combined to synthesize musical tones.
Among the electronic musical instrument of this type may be mentioned a system in which amplitude values of a musical tone waveform at successive sampling points are calculated according to the following equation 1 to produce a musical tone. ##EQU1## where q: a positive integer
X.sub.o (qR): amplitude value of a musical tone waveform at each sampling point PA1 R: value proportional to the frequency (tone pitch) of the generated musical tone (hereinafter called a frequency information) PA1 n: orders of respective harmonic wave components including fundamental wave, where PA1 C.sub.n : amplitude coefficients for harmonic wave components at respective orders (Fourier coefficients) PA1 N: number of successive sampling points of one musical tone wave at the highest frequency of the generated musical tone PA1 W:total number of the harmonic waves to be synthesized at each sampling point, the relationship between N and W is W=N/2.
n=1 corresponds to the fundamental wave (fundamental tone) PA2 n=2 corresponds to the second harmonic wave PA2 n=3 corresponds to the third harmonic wave
In the following description, the term harmonic wave includes the fundamental wave so that the fundamental wave is expressed as the first harmonic wave.
One example of an electronic musical instrument of a harmonic synthesis type is disclosed in U.S. Pat. No. 3,809,786 to Ralph Deutsch dated May, 7, 1974 under the title of Computor organ.
However, according to the prior art electronic musical instrument of the harmonic wave synthesizing system, the musical tone is generated at a frequency correponding to the tone pitch of a depressed key, with a tone color set by a harmonic wave amplitude coefficient C.sub.n stored in a harmonic wave coefficient memory device and imparted with an amplitude envelope. To synthesise such a musical tone, it is necessary to compute amplitude values F.sub.n of all (W) harmonic wave components including the first to Wth harmonic waves. With this method, however, the number of orders of the harmonic wave component to be calculated for the purpose of synthesizing a musical tone is up to the Wth order, so that it has been impossible to generate harmonic wave components higher than this order. Accordingly, it has been impossible to generate a musical tone having a tone color containing harmonic wave components of extremely high orders (for example, higher than Wth order). Where it is desired to produce a musical tone having a tone color containing harmonic wave components of the orders higher than the Wth order, it takes a longer time for mathematically processing to form the desired musical tone thus decreasing the performance efficiency of the electronic musical instrument. To limit the mathematical processing time to be less than a predetermined time it is necessary to either shorten the period of the clock pulse or to proceed the mathematical operations in parallel, thus complicating the contruction.
Another solution of this problem is disclosed in U.S. Pat. No. 3,992,971 to Masanobu Chibana, et al, dated Nov. 23, 1976 under a title of "Electronic Musical Instrument" wherein the amplitude values of the harmonic wave components of the adjacent orders are calculated simultaneously by noting the fact that the levels (amplitude coefficients) of the harmonic components of adjacent orders are nearly equal. With this method, however, although it is possible to generate harmonic wave components up to high orders without complicating the circuit construction, as the harmonic wave amplitude coefficients of adjacent orders are averaged it becomes impossible to generate musical tones of high quality and delicate tone color.